What is the common difference of a 57-term arithmetic sequence where the first term is -25 and the sum is 17,727?

Question

anonymous · Answer

first we need a formula to show the sum...

$$S = \frac{ n(t _{1} + t _{n}) }{ 2 }$$

anonymous · Answer

which "n" is the number of the terms , "t1" = the first term and "tn" = the last (or the n term)

anonymous · Answer

So I got 647 for n...what next? @PFEH.1999

anonymous · Answer

how did u find tn?

anonymous · Answer

i meant tn...that's 647

anonymous · Answer

n was 57

anonymous · Answer

@PFEH.1999

anonymous · Answer

ok let me check it.

anonymous · Answer

yess correct , tn = 47 and   $ t _{n} = t _{1} + (n-1) d$ and d is the common difference

anonymous · Answer

@ambiguousmathstudent have you want d or not?

anonymous · Answer

I got a weird answer, i think i did it wrong. i have 47=-25+(57-1)d and i got a weird answer when i solved for d

anonymous · Answer

the answer should be one of these:
11
	11.5
	12
	12.5

anonymous · Answer

47??? tn = 647 !

anonymous · Answer

hahahhaa my bad...i have awful handwriting. let me try that again

anonymous · Answer

wait i still got -2.16 which isnt an answer @PFEH.1999

anonymous · Answer

647 + 25 = 672 = 56d so d = 672/56b = 12 ;)

anonymous · Answer

you've made a mistake ;)

anonymous · Answer

ohhhhh i see what i did wrong, thank you so much. you're the best ((:

anonymous · Answer

you're welcome ;)
thank u ;) :)